A rocket is projected vertically upwards in a uniform gravitaional field. Set up and integrate the equations of motion to obtain relation between the mass of the rocket and the velocity. You may assume that the mass is being loss at a constant rate due to gases escaping from the rocket with constant velocity $v^\prime$ relative to the rocket. For the rocket starting initially from rest, ith $v^\prime = 6800~$ft/sec and a mass lost per sec equal to $1/60$th of the initial mass show that in order to reach escape velocity the ratio of weight of the fuel to the weight of the empty rocket must be almost 300!
Goldstein
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4727:Diamond Point